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The coefficient of variation is defined as the ratio of S.D to mean, a dimensionless number which on multiplication by 100 gives the percentage of dispersion with mean. But when we square this coefficient of variation, what does it signify?

(I have to understand a graph having squared coefficient of variation on y axis and mean on x axis for Poisson distributed data).

Thanks

whuber
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bioinformatician
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    The coefficient of variation is $\frac{\text{sd}(X)}{\text{mean}(X)}$. This is the same as $\text{sd}(\frac{X}{\text{mean}(X)})$. If you square this you just get the variance of $\frac{X}{\text{mean}(X)}$, i.e. X expressed in units of $\text{mean}(X)$. Does this help you? – Erik Apr 24 '12 at 07:17
  • I am just a beginner... I want to confirm my basic understanding (1) suppose i have four numbers i.e 5,7,9,11 (2) mean of these numbers comes out to be 8 (3) variance calculated as (8-5)^2 + (8-7)^2 + (8-9)^2 + (9-11)^ / 4 = 5 and the S.D is underroot of 5 i.e 2.23 (5) the coefficient of variation : 2.23/mean(=8) will be .2795 (6) if i square .2795 , i get ~ .078 ... so how to comprehend this .078 in terms of my data (5,7,9,11) ? – bioinformatician Apr 24 '12 at 08:34
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    Are you sure this is a squared CV and not the ratio of the sample variance to the sample mean? For a Poisson distribution, this ratio should be close to 1, so it could make sense to plot it against the mean as a check for departures from "Poissonness": the plot should be approximately level. Plotting the squared CV would instead produce a hyperbolic curve, which is not a good visual reference for exploring and understanding data. – whuber Apr 24 '12 at 13:12
  • This is not an answer but I am not allowed to comment yet. I am also perplexed by the widespread use of this metric in bioinformatics. This recent paper is one of many which uses it to visualize technical noise.... ??? http://www.nature.com/nrg/journal/v16/n3/fig_tab/nrg3833_F2.html – gaelgarcia Mar 06 '15 at 01:13
  • @whuber may I ask why you used SCV instead of CV in the DESeq paper? – gkcn Aug 14 '15 at 10:09
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    I can't post this as a comment as I don't have a high enough reputation yet, but in reply to @gkcn, I believe this is a different W Huber. whuber is a William, and the DESeq author is a Wolfgang. – aedanr Mar 27 '17 at 01:34

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